# Inductor with controlled temperature coefficient

Let's assume we have an air-spaced inductor made of copper wire.

As temperature changes, due to thermal expansion of physical dimensions of the coil, its inductance changes too.

1) Is there a way to control the thermal coefficient of inductance somehow (like using some clever coil shape or something)? I would love to be able to tune the temperature coefficient in the range $\pm 30\:\rm{ppm/C}$.

2) Is there a way at least to make the temperature coefficient significantly lower than the coefficient of thermal expansion of copper ($<10\:\rm{ppm/C}$)?

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I am not sure whether you can optimize the shape to reduce the influence of thermal expansion. What often helps for high precision instruments is a precise temperature control. You heat up the important bits to a value above room temperature and try to keep it exactly at, for example, 35°C. With only tiny temperature variations remaining, the influence on the dimensions is also reduced by orders of magnitude compared to a normal instrument where the inductor is operating in a wide temperature range (18-30°C, depending on room temperature). –  Alexander Mar 20 '12 at 16:34
The active temperature control that @Alexander suggests is a common strategy...even for vacuum filled instruments like the precision beam current monitors used at JLAB because changes in the size of the instrument affect their gain. –  dmckee Mar 20 '12 at 16:58
I am already in oven-controlled environment. My goal here is to match temperature coefficient of inductor to ones of other pieces of the circuit to lower temperature impact even further. –  BarsMonster Mar 21 '12 at 3:01
If that doesn't work, it seems to me that your only choice is to use a core which is not air (or at least, not entirely air). You could look for something with temperature-dependent $\mu$, to take an obvious example. Or something where $\mu \neq 1$ but that expands in a different way than the copper. I'm not sure what your constraints are for the core.